Despite vast advances in set theory and mathematics in general, the
language of set theory, which is also the language of mathematics, has
remained the same since the beginning of modern set theory and first
order logic. That formal language has served us very well, but it is of
necessity limited, and time has come to extend it.
I have written a paper to extend the language of set theory and to
resolve some of its incompleteness. The paper is available at
http://web.mit.edu/dmytro/www/NewSetTheory.htm
Meaningfully extending the language of set theory opens new horizons for
mathematicians, but any such endeavor also raises a host of
philosophical issues. I plan to discuss some of the issues in future
FOM postings.
Questions, comments, suggestions, and criticisms about the paper are
welcome. The paper is still a draft, so it may contain incomplete
explanations and stylistic flaws.
Sincerely,
Dmytro Taranovsky